6, we compare the number of samples for each category of discrete columns between real data and fake data generated by the continuous and discrete diffusion models. 4.2.3 Sampling TimeĪs shown in Table 4, in all cases, the F1 and coverage scores of the fake data by the discrete diffision model are better than those of the continuous diffusion model. Table 2: Summarized sampling diversity results. Table 3: Summarized sampling time results. In Stroke, TableGAN and CTGAN show good performance in terms of the sampling quality, however, CoDi outperforms by large margins in terms of the diversity. However, CoDi exceeds other methods and particularly performs well in multi-class classification and regression datasets, as shown in Tables 13 and 14 of Appendix E.2. Among the baselines, MedGAN and VEEGAN show poor performance, whereas TableGAN and STaSy show reliable diversity to some extent. Table 3 shows the averaged coverage scores across the datasets. To evaluate the diversity of the fake data, we use coverage, which is the ratio of fake samples that have at least one real sample within their 5 t h nearest neighborhoods. We highlight the best results in light blue, and the second best with underline. We report averaged scores across the datasets. Table 1: Summarized experimental results in terms of sampling quality. After sampling, we post-process the continuous and discrete outputs, using the reverse scaler and Argmax function, respectively. At this point, x C i − 1 and x D i − 1 are conditioned on both denoised samples in continuous and discrete models at the previous time step i. Firstly, we sample each noisy vector from the corresponding prior distribution, and convert the noises into fake samples through T steps.

The detailed sampling process of our method is in Algorithm 2. The former focuses on synthesizing minority class(es) in classification data, while the latter generates the entire data. SOS (Kim et al., 2022b) and STaSy (Kim et al., 2022a) are state-of-the-art tabular data synthesis methods, which are based on the score-based generative regime.

OCT-GAN (Kim et al., 2021) is a generative model based on neural ODEs. In specific, they approximate the discrete variables to the continuous spaces by using Gumbel-Softmax. CTGAN and TVAE (Xu et al., 2019) propose a column-type-specific pre-processing method to deal with the challenges in tabular data, for which tabular data usually consists of mixed-type variables and the variables follow multi-modal distributions. TableGAN (Park et al., 2018) utilizes convolutional neural networks to improve the quality of synthesized tabular data and prediction on label column accuracy. With great advancement in generative modeling, there exists an attempt to synthesize tabular data using GANs. On the other hand, Bayesian networks (Zhang et al., 2017 Aviñó et al., 2018) and decision trees (Reiter, 2005) can be used for discrete variables. ( 2016) utilizes a recursive table modeling with a Gaussian copula for synthesizing continuous variables. There are many tabular data synthesis methods to create realistic fake tables for various purposes. The most common way to treat discrete variables is to sample in continuous spaces after their one-hot encoding (and sometimes via Gumbel-softmax) (Xu et al., 2019 Kim et al., 2021, 2022b, 2022a), which may lead to sub-optimal results due to sampling mistakes. While various processing methods for continuous variables have been proposed, e.g., standardizing continuous values using variational Gaussian mixture models (Xu et al., 2019) and applying the logarithm transformation to treat long-tailed distributions (Zhao et al., 2021), handling discrete variables remains challenging. Due to the complicated nature of tabular data, pre/post-processing of the tabular data is inevitable, and the performance of tabular data synthesis methods is highly dependent on the pre/post-processing method. To be specific, tabular data usually consists of mixed data types, i.e., continuous and discrete variables. In spite of the advancement, there still exists a challenging issue in the current state-of-the-art tabular data synthesis methods.

Cody tabular data